Department of Biostatistics and Bioinformatics, Duke University, Durham, North Carolina, USA.
Stat Med. 2018 Nov 30;37(27):3904-3917. doi: 10.1002/sim.7847. Epub 2018 Jun 10.
Grouped survival data arise often in studies where the disease status is assessed at regular visits to clinic. The time to the event of interest can only be determined to be between two adjacent visits or is right censored at one visit. In data analysis, replacing the survival time with the endpoint or midpoint of the grouping interval leads to biased estimators of the effect size in group comparisons. Prentice and Gloeckler developed a maximum likelihood estimator for the proportional hazards model with grouped survival data and the method has been widely applied. Previous work on sample size calculation for designing studies with grouped data is based on either the exponential distribution assumption or the approximation of variance under the alternative with variance under the null. Motivated by studies in HIV trials, cancer trials and in vitro experiments to study drug toxicity, we develop a sample size formula for studies with grouped survival endpoints that use the method of Prentice and Gloeckler for comparing two arms under the proportional hazards assumption. We do not impose any distributional assumptions, nor do we use any approximation of variance of the test statistic. The sample size formula only requires estimates of the hazard ratio and survival probabilities of the event time of interest and the censoring time at the endpoints of the grouping intervals for one of the two arms. The formula is shown to perform well in a simulation study and its application is illustrated in the three motivating examples.
分组生存数据在研究中经常出现，其中疾病状态在定期就诊时进行评估。感兴趣事件的时间只能确定为两次相邻就诊之间，或者在一次就诊时被右删失。在数据分析中，用分组区间的终点或中点替换生存时间会导致组间比较的效应大小的有偏估计。Prentice 和 Gloeckler 为分组生存数据的比例风险模型开发了一个最大似然估计器，该方法已被广泛应用。以前关于分组数据研究设计的样本量计算的工作是基于指数分布假设或替代假设下的方差近似，而不是基于零假设下的方差。受 HIV 试验、癌症试验和体外实验研究药物毒性的启发，我们为分组生存终点的研究开发了一个样本量公式，该公式使用 Prentice 和 Gloeckler 方法在比例风险假设下比较两个臂。我们不施加任何分布假设，也不使用检验统计量方差的任何近似值。样本量公式仅需要两个臂之一的感兴趣事件时间和分组区间终点的删失时间的危险比和生存概率的估计值。该公式在模拟研究中表现良好，并且在三个动机示例中说明了其应用。
